Um, yes. By definition, that is precisely what the offense does, and is in fact the object of the game.
Yup In ncaa, nfl, high school or pretty much any other type of football the offense must advance the ball 10 yards in 4 downs to earn a new set of downs.
College football players that have been drafted into the nfl, must complete mini-camp to advance on to the nfl.
Quarterbacks are an important part of the offense team in football. There are no quarterbacks that have played in the NFL that attended the Airforce Academy.
Defense Coordinators and Offense Coordinators advise the coach on the field over radio.
"No player on offense may assist a runner except by blocking for him." -From NFL rules digest.
Both the offense and defense can score on a blocked field goal. The defense can recover a blocked field goal and advance it regardless of where they recover it. The offense can recover a blocked field goal and advance it as long as the ball has not passed the original line of scrimmage.